The blow-up for weakly coupled reaction-diffusion systems

Wang, Liwen

doi:10.1090/S0002-9939-00-05860-3

The blow-up for weakly coupled reaction-diffusion systems
HTML articles powered by AMS MathViewer

by Liwen Wang

Proc. Amer. Math. Soc. 129 (2001), 89-95

DOI: https://doi.org/10.1090/S0002-9939-00-05860-3

Published electronically: August 17, 2000

PDF | Request permission

Abstract:

In this paper we consider a weakly coupled parabolic system with nonnegative exponents in the forcing functions. We find the conditions which result in blow-up in finite time. Also, we obtain the blow-up rate.

References

Deng, K., Blow-up rates for parabolic systems, Z. Angew Math. Phys., 46, 110-118 (1995).
Escobedo, M. and Herrero, M. A., Boundedness and blowup for a semilinear reaction-diffusion system, J. Diff. Equ., 89, 176-202 (1991).
Miguel Escobedo and Howard A. Levine, Critical blowup and global existence numbers for a weakly coupled system of reaction-diffusion equations, Arch. Rational Mech. Anal. 129 (1995), no. 1, 47–100. MR 1328471, DOI 10.1007/BF00375126
Avner Friedman and Yoshikazu Giga, A single point blow-up for solutions of semilinear parabolic systems, J. Fac. Sci. Univ. Tokyo Sect. IA Math. 34 (1987), no. 1, 65–79. MR 882125
Avner Friedman and Bryce McLeod, Blow-up of positive solutions of semilinear heat equations, Indiana Univ. Math. J. 34 (1985), no. 2, 425–447. MR 783924, DOI 10.1512/iumj.1985.34.34025
Galaktionov, V. A., Kurdyumov, S. P., and Samarskii, A. A., A parabolic system of quasilinear equations, I Differential Equations 21, 1049-1062 (1985).
Galaktionov, V. A., Kurdyumov, S. P., and Samarskii, A. A., A parabolic system of quasilinear equations. II Differential Equations 19, 1558-1571 (1983).
Bei Hu and Hong-Ming Yin, The profile near blowup time for solution of the heat equation with a nonlinear boundary condition, Trans. Amer. Math. Soc. 346 (1994), no. 1, 117–135. MR 1270664, DOI 10.1090/S0002-9947-1994-1270664-3
Pao, C.-V., Nonlinear Parabolic and Elliptic Equations Plenum Press, New York 1992.
Julio D. Rossi, The blow-up rate for a system of heat equations with non-trivial coupling at the boundary, Math. Methods Appl. Sci. 20 (1997), no. 1, 1–11. MR 1429327, DOI 10.1002/(SICI)1099-1476(19970110)20:1<1::AID-MMA843>3.0.CO;2-E
Alexander A. Samarskii, Victor A. Galaktionov, Sergei P. Kurdyumov, and Alexander P. Mikhailov, Blow-up in quasilinear parabolic equations, De Gruyter Expositions in Mathematics, vol. 19, Walter de Gruyter & Co., Berlin, 1995. Translated from the 1987 Russian original by Michael Grinfeld and revised by the authors. MR 1330922, DOI 10.1515/9783110889864.535
Wang L., The blow-up for a semilinear parabolic system. Mathematica Applicata (complement), 104-106 (1995).
Zhang, K., On the blow-up rate of solution of semilinear parabolic equations system, J. Math. Study 27, No. 2, 102-108(1994).
Ke Nong Zhang, Blow-up phenomena in solutions of systems of semilinear parabolic equations, J. Math. Res. Exposition 15 (1995), no. 1, 83–90 (Chinese, with English and Chinese summaries). MR 1334260